Can the new resonance at LHC be a CP-Odd Higgs boson?

A plausible explanation of the recent experimental indication of a resonance in the two-photon spectrum at LHC is that it corresponds to the CP-odd Higgs boson. We explore such a possibility in a generic framework of the two Higgs doublet models (2HDM), and combine $m_A \approx 750$GeV with the known $m_h =125.7(4)$~GeV to show that the charged Higgs boson and the other CP-even scalar masses become bounded from bellow and from above. We show that this possibility is also consistent with the electroweak precision data and the low energy observables, which we test in a few leptonic and semileptonic decay modes.


Introduction
In addition to the Higgs boson, m h = 125.7(4) GeV [1], the experiments at LHC recently indicated a possibility for a resonance in the diphoton spectrum at about 750 GeV [2]. While its spin must be either J = 0 or 2, its parity cannot be yet assessed. If, after improving statistics and further examining systematics of the data sample, this signal remains as such, a plausible explanations for the newly observed state could be the ones offered in refs. [3][4][5][6][7][8][9][10][11][12][13].
The simplest possibility is to consider scenarios with two Higgs doublets (2HDM) in which the spectrum of scalars consists of two CP-even (h and H), one CP-odd (A) and one charged Higgs state (H ± ). In this paper, we focus on the possibility of the new state being the CP-odd Higgs and find that the general theoretical constraints combined with the two known masses result in the bounds on the remaining two Higgs boson states. We also show that the resulting bounds and the proposed scenario satisfy the electroweak precision tests, and do not significantly modify the low energy (semi-)leptonic decay modes.
Let us stress that, in a pure 2HDM, the production cross section for the heavy spin-0 states seems to be too low to explain the claimed excess of σ(gg → X)B(X → γγ), where X stands for the new 750 GeV resonance, in such a way that an extended particle content might be needed [8]. However, our conclusions on the spectrum of the model are unlikely to be significantly affected by the additional particles as long as they are fermions. 1 One should be cautious and study carefully the signal strength, including the background contamination in the signal region as well as the possible signal-background interference, which in general are model dependent [14]. It should be reemphasized that other possibilities can be envisaged, such as the one in which H and A are mass degenerate. In this paper, we focus on the possibility of A being the desired state hinted at about 750 GeV.

General Constraints on 2HDM and the Spectrum of Higgses
The most general CP-conserving 2HDM potential compatible with gauge symmetries of the Standard Model is given by (see eg. ref. [15]), where Φ 1 and Φ 2 are the two complex scalar SU (2) doublets with hypercharge Y = +1. In the above expression the Z 2 symmetry (Φ 1,2 → −Φ 1,2 ) has been tacitly assumed, except for the soft symmetry breaking term proportional to m 2 12 . Assuming that each doublet carries a non-zero vacuum expectation value (vev) one can write, with both vev's v 1,2 being associated with the neutral components to avoid a problem of breaking the U (1) symmetry of electromagnetism. A further assumption is the conservation of CP-symmetry in the Higgs sector which translates to v 1,2 ∈ R. Two of the six fields (φ + 1,2 , ρ 1,2 , η 1,2 ) are Goldstone bosons and can be gauged away, which then leaves us with the physical spectrum consisting of one charged H ± , two CP-even neutral h, H, and one CP-odd neutral A boson, that are linear combinations of the above fields, namely, with α and β associated with rotations that diagonalize the mass matrices. Written in terms of parameters given in V (Φ 1 , Φ 2 ) one gets, where λ 345 ≡ λ 3 + λ 4 + λ 5 . After setting v 2 1 + v 2 2 ≡ v SM = 246.2 GeV (which in the following will be referred to as v), tan β becomes the free model parameter and the quartic couplings λ 1−5 can be expressed in terms of scalar masses and mixing angles as [16]: in an obvious notation in which we also replaced M 2 ≡ m 2 12 sin β cos β . Conversely, To ensure that the scalar potential is bounded from below, the quartic parameters in Eq. (1) should satisfy [17] Stability of the vacuum (∂V /∂v 1,2 = 0) amounts to solving which cannot be done analytically for m 12 = 0. Instead, one can derive a condition that is necessary and sufficient for V (Φ 1 , Φ 2 ) to have a global minimum at (v 1 , v 2 ) and it reads [18], Another generic constraint comes from the requirement of unitarity of the S-wave component of the partial wave decomposition of the full Higgs scattering amplitudes. That condition can be translated into a set of constraints on the quartic couplings in Eq. (1), which amounts to [19] |a ± |, |b ± |, |c ± |, |f ± |, |e 1,2 |, |f 1 |, |p 1 | < 8π, where We then generate random points in the parameter space by fixing m h = 125.7(4) GeV, v = 246.22 GeV, as well as m A = 750(30) GeV, and by varying to select those that are consistent with constraints given in Eqs. (7)(8)(9)(10). Two interesting results of our scan are shown in Fig. 1 where we see that the lower values of tan β are highly favored with most of the points being tan β 5, and that the mass of the other two Higgs states are bounded both from below and from above, namely, Furthermore we observe that the Z 2 -symmetry breaking term cannot be excessively large and it reproduces m A = 750(30) GeV, for |M | ∈ (200, 800) GeV. Finally the resulting points are concentrated in the region of | cos(β − α)| 0.3, which then means that the couplings g hV V > g HV V for V being either W or Z. 2 This result agrees with the findings of ref. [20].
Another interesting feature is that one cannot impose the degeneracy m h = m H and scan over the parameter space as indicated above (but without fixing m A ). While most of tan β points remain small, the values of cos(α − β) are equidistributed between −1 and 1, but one then gets an upper bound on m A 700 GeV, inconsistent with the state supposedly observed at LHC. We should also mention that the direct experimental searches of the non-Standard Model Higgs states also restrict cos(α − β) to small values, as recently discussed in Refs. [21,22].

Including fermions
As it is well known, in order to avoid the tree level flavor changing neutral currents (FCNC), one imposes that the fermions of definite charge and chirality couple to a specific Higgs doublet. In this way one distinguishes various types of 2HDM: In Type I models all fermions couple to the same Higgs doublet (Φ 2 , by convention); In Type II the right-handed (RH) quarks with charge Q = 2/3 couple to the doublet Φ 2 , whereas those with Q = −1/3 to the doublet Φ 1 . A slight modification of the latter rule leads to two other types: Type X 2HDM (or lepton-specific), and type Z (or flipped) one. Their coupling patterns to quarks and leptons are listed in Tab. 1. More general, in terms of Yukawa couplings, is the so called Type III 2HDM in which the couplings to fermions are all to be fixed by the data [23] which is often impractical because of too many free parameters so that one has to resort to additional assumptions such as minimal flavor violation (MFV) [24,25], the natural flavor conservation [26], or the aligned 2HDM [27] where the minimal flavor violation is ensured by assuming proportionality between the matrices of Yukawa couplings to the two Higgs doublets.
Model The Yukawa interaction Lagrangian for the neutral currents can be written as [15], where the sum runs over up-and down-type quarks, as well as leptons. Here we focus on the coupling C Af which depends on tan β and is given for various types of 2HDM in Tab. 2. With this in mind, the expression for the decay width of the CP-odd Higgs to  (14) for the models of type I, II, Lepton-specific (X) and Flipped (Z) [15].
two fermions reads, where N c = 3 for quarks, and 1 otherwise. Quite obviously the full width Γ(A) will be highly dominated by the top quark. As for the decay to two photons, one has [28], where the triangle loop induces the factor, The expression for the decay width of A → Zγ reads [29], and its contribution to the full decay width is smaller than the other modes discussed above.
In Fig. 2 we plot the partial decay width for A → tt, A → bb, A → τ τ , A → γγ and A → Zγ for all four types of the 2HDM discussed here. As expected, the A → tt mode is largely dominant and essentially saturates the width of the CP-odd Higgs boson, Γ(A), the results of which are given in Tab. 3 for four different values of tan β. Since the experimenters are searching for the A → τ τ mode, in the same table we also give the values of B(A → τ τ ) for all four types of 2HDM considered here. It is worth emphasizing that for small values of tan β the width Γ(A) is quite large and can accommodate the observation made by ATLAS, namely that the better fits are obtained for the new resonance having a width ∼ 40 GeV. Similar conclusion holds true for the H boson, the coupling of which to tt is proportional to 1/ tan β for small cos(β − α).
Finally, with the above ingredients we can also compute the dominant decay channel H ± → tb, the decay width of which is given by, while for the leptonic decay we have    The results for the branching fraction B(H ± → τ ν τ ) are given in Tab. 3. Before concluding this Section we would like to emphasise once again that the bounds on the Higgs states are derived by considering the general theoretical arguments. The most significant bound comes from the tree-level unitarity constraints (10), and the effects of heavy fermions (beyond the Standard Model) would enter only through loops and are therefore unlikely to significantly alter the statements we made about the Higgs states.

Electroweak Precision Tests
As it is well known, the additional scalar states present in a 2HDM contribute to the gauge bosons vacuum polarizations, and are as such constrained by electroweak precision data. The scalar contributions to the Peskin-Takeuchi parameters S, T , and U for the 2HDM case can be found e.g. in ref. [30]. In order to compute the related bounds on the spectrum, composing the χ 2 function as with X i = ∆S, ∆T, ∆U and the covariance matrix σ 2 ij ≡ σ i V ij σ j , in which (σ 1 , σ 2 , σ 3 ) = (0.11, 0.13, 0.11).
In Fig. 3 we show the region allowed at 99% CL by electroweak precision data in the plane m H versus m H ± . Since the coupling between the additional scalars and the gauge bosons depend on cos(β − α) (see footnote 2), we present two representative cases: cos(β − α) = 0 and cos(β − α) = 0.3, which according to Sec. 2, are the minimum and maximum value allowed by our scan. Note that most of the points which were previously allowed, Fig. 1, are still not excluded. Let us stress that, as already pointed out in the introduction, additional states which may be needed to increase the production cross section σ(gg → A) may affect significantly Fig. 3, but in a model dependent way. The analysis of the electroweak precision measurements in these extended models must be done case by case, and is beyond the scope of the paper.

Low energy physics observables
Since the charged Higgs boson is now fully bounded [cf. Eq.(13)], the contribution from the charged Higgs can modify the low energy decay rates of the leptonic and semileptonic processes which generally agree with the Standard Model predictions within the error bars. To that end we add a term involving the couplings to the scalar sector to the effective Hamiltonian of the Standard Model at low energies, namely where u and d stand for the generic up-and down-type quark flavor. Using this Hamiltonian one can easily compute the semileptonic and the leptonic decay rates for the specific channels, e.g. B → Dτ ν τ and B → τ ν τ , and we obtain with τ B being the B-meson lifetime, and The decay constant (f B ) and the form factors [f +,0 (q 2 )] are defined via, Notice that we consider the pseudoscalar to pseudoscalar meson decay for which the decay form factors are better controlled through numerical simulations of QCD on the lattice [32].
As it can be seen from the above expressions, for g S,P = 0 the helicity suppression is lifted and the contribution coming from coupling to the charged scalar could be important. The explicit expressions for g S,P , in terms of the quark and lepton masses as well as m H ± and tan β, in various types of 2HDM read: measured in three experiments [36][37][38] leading to an average of R D = 0.41 (5). That result is consistent with the SM value, R SM D = 0.31(2) [39], at less than 2σ-level and also with the 2HDM scenarios discussed here. Like in the case of leptonic decay, only in the Type II model at moderately large values of tan β one can see a small deviation with respect to the Standard Model, as shown in Fig. 4. That deviation is however too small to be probed experimentally for tan β < 15. As for the loop induced processes, one extra constraint can be obtained from the comparison between the experimentally established B(B s → µ + µ − ) exp = 2.8 +0.7 −0.6 × 10 −9 [40] with the Standard Model prediction [41] leading to Using, instead of the Standard Model, the expressions for Wilson coefficients computed in a generic 2HDM [42] leads to the exclusion bound on the very low tan β 0.7, as shown in Fig. 4.

Conclusion
In this paper we showed that the CP-odd Higgs is a plausible candidate for the resonance From our scan, in which we used the general constraints spelled out in Eqs. (7-10), we also find that the preferred values of tan β are relatively small, tan β < 15, with most of the points concentrated in the region tan β < 5. The width of the CP-odd Higgs is dominated by the A → tt mode and its value significantly depends on tan β. We find that the width can be large [as large as Γ(A) 40 GeV, for tan β = 1]. Furthermore, we find that | cos(β − α)| 0.3, i.e. not far from the Standard Model, and in agreement with the results of the SFitter analysis [20], and with the direct searches [21,22]. We then checked that for the range of tan β and m H ± obtained from our scan, the semileptonic and leptonic decay modes are not significantly modified with respect to the Standard Model predictions. We also checked that the spectrum of the 2HDM considered here is fully consistent with electroweak precision data encoded in the S, T , U parameters.
The plots, in which all the constraints considered in this paper are included, are presented in Fig. 5. Notice in particular that B(B → τ ν τ ) and R D provide very similar bounds in the (tan β, m H ± ) plane for m H ± ∈ (0.4, 1) TeV. They, at best, exclude the large values of tan β in the Type II model, otherwise they are insensitive to the parameter space (small tan β) we are considering here. B(B s → µ + µ − ), instead, provides an important constraint, i.e. exclusion of the very small values of tan β. Since that last constraint involves coupling to the top-quark, it is independent of the type of the 2HDM.  Fig. 1: we see that the electroweak precision data further restrict the region of allowed masses although, broadly speaking, the bounds we derived in Sec. 2 remains unchanged.
Finally, we need to stress once again that our ambition was not to provide a full scenario of physics beyond the Standard Model. Rather, we merely attempt whether or not the recent experimental hint of the excess at LHC can be consistent with the interpretation of the CP-odd Higgs in the general framework of 2HDM. We find that scenario plausible and the repercussions on the remaining Higgs bosons look quite appealing because they can be either confirmed or refuted experimentally quite soon. Since the announcement of the LHC results [2] many authors discussed σ(gg → X)B(X → γγ), where X stands for the resonance we claim to be consistent with the CP-odd Higgs, being larger than expected in the 2HDM alone. At this point one should be careful about interpretation of such results because: (a) they are not published or publicly announced, and (b) a careful study of the signal strength and of the signal-background interference, including the appropriate cuts, is mandatory. The conclusion we reached here is solely based on considerations of the spectrum of scalars and it cannot be significantly changed in the presence of additional fermionic degrees of freedom, assuming the mixing between the Standard Model fermions and the extra heavy fermions is indeed small.